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JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank Critical Thinking

  • question_answer
    An electric dipole is situated in an electric field of uniform intensity E whose dipole moment is p and moment of inertia is I. If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is [MP PET 2003]

    A)            \[{{\left( \frac{pE}{I} \right)}^{1/2}}\]

    B)                                      \[{{\left( \frac{pE}{I} \right)}^{3/2}}\]

    C)            \[{{\left( \frac{I}{pE} \right)}^{1/2}}\]                           

    D)            \[{{\left( \frac{p}{IE} \right)}^{1/2}}\]

    Correct Answer: A

    Solution :

     When dipole is given a small angular displacement q  about it's equilibrium position, the restoring torque will be \[\tau =-\,pE\sin \theta =-\,pE\theta \]     (as sinq = q) or \[I\frac{{{d}^{2}}\theta }{d{{t}^{2}}}=-pE\theta \]    (as \[\tau =I\alpha =I\frac{{{d}^{2}}\theta }{d{{t}^{2}}}\]) or \[\frac{{{d}^{2}}\theta }{d{{t}^{2}}}=-{{\omega }^{2}}\theta \] with \[{{\omega }^{2}}=\frac{pE}{I}\] Þ \[\omega =\sqrt{\frac{pE}{I}}\]


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